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Boundedness of fractional Hankel wavelet transform on some Beurling type spaces

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Abstract

We give certain characterization results of fractional Hankel transform on the spaces of type Beurling-Bjorck. Using wavelet theory, we obtain certain boundedness results of continuous wavelet transform in terms of fractional Hankel transform on the Beurling-Bjorck type spaces.

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References

  1. Arteaga, C., and I. Marrero. 2021. Structure, boundedness, and convergence in the dual of a Hankel-\(K{M_p }\) space. Integral Transforms and Special Functions 32 (3): 174–190.

    Article  MathSciNet  MATH  Google Scholar 

  2. Belhadj, M., and J.J. Betancor. 2001. Hankel transformation and Hankel convolution of tempered distributions. The Rocky Mountain journal of mathematics 3 (4): 1171–1203.

    MathSciNet  MATH  Google Scholar 

  3. Beurling, A. 1961. Quasi-Analyticity and General Distributions, Lecture 4 and 5. Stanford: AMS Summer Institute.

    Google Scholar 

  4. Bjorck, G. 1966. Linear partial differential operators and generalised distributions. Arkiv for Matematik 6 (21): 351–407.

    Article  MathSciNet  MATH  Google Scholar 

  5. Carmichael, R.D., R.S. Pathak, and S. Pilipovic. 1993. Holomorphic functions in tubes associated with ultradistributions. Complex Variables and Elliptic Equations 21 (1–2): 49–72.

    MathSciNet  MATH  Google Scholar 

  6. Debnath, L. 2002 Wavelet Transform and Their Applications. Birkh\(\ddot{a}\)user, Boston, MA.

  7. Daubechies, I. 2006 Ten Lectures on Wavelets. In: CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM Publ., Philadelphia, PA.

  8. Hirschman, I.I. 1960. Variation diminishing Hankel transform. Journal Analyse d’Mathematique 8: 307–361.

    Article  MathSciNet  MATH  Google Scholar 

  9. Shi, J., N. Zhang, and X. Liu. 2012. A novel fractional wavelet transform and its application. Science China Information Sciences 55 (6): 1270–1279.

    Article  MathSciNet  MATH  Google Scholar 

  10. Kaiser, G. 1994. A Friendly Guide to Wavelets. Boston: Birkhauser.

    MATH  Google Scholar 

  11. Kerr, F.H. 1992. Fractional powers of Hankel transforms in the Zemanian space. Journal of mathematical analysis and applications 166: 65–83.

    Article  MathSciNet  MATH  Google Scholar 

  12. Linares, M., and J.M.R. Prez Mendez. 1991. A Hankel type integral transformation on certain space of distributions. Bulletin of the Calcutta Mathematical Society 83: 447–546.

    MathSciNet  MATH  Google Scholar 

  13. Mahato, K. 2018. The composition of fractional Hankel wavelet transform on some function spaces. Applied Mathematics and Computation 337: 76–86.

    Article  MathSciNet  MATH  Google Scholar 

  14. Mahato, K., and P. Singh. 2019. Continuity of the fractional Hankel wavelet transform on the spaces of type S. Mathematical Methods in the Applied Sciences 42 (6): 1941–1954.

    Article  MathSciNet  MATH  Google Scholar 

  15. Mahato, K., and P. Singh. 2021. Continuity of fractional Hankel wavelet transform on the Gelfand-Shilov Spaces. Rocky Mountain Journal of Mathematics 51 (3): 963–972.

    Article  MathSciNet  MATH  Google Scholar 

  16. Morlet, J., J. Arens, F. Fourgeau, and D. Giard. 1982. Wave propagation and sampling theory-Part II: Sampling theory and complex waves. Journal of Geophysics 47: 222–236.

    Article  Google Scholar 

  17. Mendlovic, D., Z. Zalevsky, D. Mas, J. Garcia, and C. Ferreira. 1997. Fractional wavelet transform. Applied optics 36 (20): 4801–4806.

    Article  Google Scholar 

  18. Pandey, J.N. 2011. Wavelet transforms of Schwartz distributions. Journal of Computational Analysis and Applications 13 (1): 47–83.

    MathSciNet  MATH  Google Scholar 

  19. Pathak, R S. 2009. The Wavelet Transform, Vol-6, Atlanis Press/World Scientific.

  20. Pathak, R.S., and M.M. Dixit. 2003. Continuous and discrete Besse wavelet transforms. Journal of Computational and Applied Mathematics 160: 211–250.

    Article  Google Scholar 

  21. Pathak, R.S., and K.K. Shrestha. 2001. The Hankel transform of Gevrey ultradistributions. Integral Transforms and Special Functions 11 (1): 61–72.

    Article  MathSciNet  MATH  Google Scholar 

  22. Pathak, R.S., and A. Singh. 2017. Wavelet transform of Beurling-Bjorck type ultradistributions. Rendiconti del Seminario Matematico della Universita di Padova 137 (1): 211–222.

    Article  MathSciNet  MATH  Google Scholar 

  23. Prasad, A., and A. Mahato. 2012. The fractional wavelet transform on spaces of type S. Integral Transforms and Special Functions 23 (4): 237–249.

    Article  MathSciNet  MATH  Google Scholar 

  24. Prasad, A., and A. Mahato. 2013. The fractional wavelet transform on spaces of type W. Integral Transforms and Special Functions 24 (3): 239–250.

    Article  MathSciNet  MATH  Google Scholar 

  25. Prasad, A., and K. Mahato. 2016. Two versions of fractional powers of Hankel-type transformations and pseudo-differential operators. Rendiconti del Circolo Matematico di Palermo Series 65 (2): 209–241.

    Article  MathSciNet  MATH  Google Scholar 

  26. Prasad, A., and K. Mahato. 2015. The fractional Hankel wavelet transformation. Asian-European Journal of Mathematics 8 (2): 1550030.

    Article  MathSciNet  MATH  Google Scholar 

  27. Singh, A., and A. Mala. 2019. The continuous wavelet transform on ultradistribution spaces. InColloquium Mathematicum 157: 189–201.

    Article  MathSciNet  MATH  Google Scholar 

  28. Singh, A., N. Raghuthaman, and R.D. Carmichael. 2022. Wavelet transform of multiplicators and convolutors for ultradistributions. Mathematical Methods in the Applied Sciences. https://doi.org/10.1002/mma.8751.

    Article  Google Scholar 

  29. Torre, A. 2008. Hankel-type integral transforms and their fractionalization: a note. Integral Transforms and Special Functions 19 (4): 277–292.

    Article  MathSciNet  MATH  Google Scholar 

  30. Upadhyay, S.K., R.N. Yadav, and L. Debnath. 2012. On continuous Bessel wavelet transformation associated with the Hankel-Hausdorff operator. Integral transforms and Special functions 23 (5): 315–323.

    Article  MathSciNet  MATH  Google Scholar 

  31. Zemanian, A.H. 1968. Generalized Integral Transformations. New York: Interscience Publishers.

    MATH  Google Scholar 

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Acknowledgements

The first author is partially supported by DST-SERB, New Delhi, India (File No-EEQ/2018/000335).

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Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Kanailal Mahato & Prashant Singh

  2. Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur, 831014, India

    Kanailal Mahato

  3. Department of Mathematics, Sri Murali Manohar Town PG College, Bailia, 277001, India

    Prashant Singh

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  1. Kanailal Mahato
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Correspondence to Kanailal Mahato.

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Mahato, K., Singh, P. Boundedness of fractional Hankel wavelet transform on some Beurling type spaces. J Anal 31, 2383–2396 (2023). https://doi.org/10.1007/s41478-023-00568-5

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